BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Giovanni Panti (Università degli Studi di Udine) DTSTART:20210114T153000Z DTEND:20210114T164500Z DTSTAMP:20260422T225717Z UID:BODS/1 DESCRIPTION:Title: Slo w continued fractions\, Minkowski functions and the joint spectral radius< /a>\nby Giovanni Panti (Università degli Studi di Udine) as part of Breme n Online Dynamics Seminar\n\n\nAbstract\nEvery unimodular partition of the real unit interval in m pieces gives\nrise to $2^m$ slow continued fracti on maps. Many such maps have names\n(Farey fractions\, ceiling fractions\, even/odd fractions\, ...)\, but most\nare nameless. Certain properties ar e commonly shared (for example\, the\nvalidity of Lagrange's theorem)\, wh ile other features are more delicate\n(the validity of the Serret theorem\ , the description of the unique a.c.\ninvariant measure\, the characteriza tion of purely periodic points\, ...).\n\nAny slow continued fraction map determines a Minkowski function\, namely\nthe distribution function of the measure of maximal entropy. These\nMinkowski functions have a well-define d average Holder exponent (studied\nby many authors\, and related to the d imension of the measure)\, as well\nas a least Holder exponent. The latter has the form log(m)/2*log(r)\,\nwith r a quadratic irrational\, the joint spectral radius of the iterated\nfunction system given by the inverse bra nches of the map.\n\nIt is plausible that every IFS with maps in $\\mathrm {GL}(2\,\\mathbb Z)$ has algebraic joint\nspectral radius\, but as far as we know this issue has not been settled.\nWe show however\, in joint work with Davide Sclosa\, that this is indeed\nthe case for IFSs over two maps in $\\mathrm{SL}(2\,\\mathbb Z_{\\geq 0})$.\n LOCATION:https://researchseminars.org/talk/BODS/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Amir Mohammadi (UC San Diego) DTSTART:20210128T153000Z DTEND:20210128T164500Z DTSTAMP:20260422T225717Z UID:BODS/2 DESCRIPTION:Title: Geo desic planes in hyperbolic 3-manifolds\nby Amir Mohammadi (UC San Dieg o) as part of Bremen Online Dynamics Seminar\n\n\nAbstract\nLet M be a hyp erbolic 3-manifold\, a geodesic plane in M is a\ntotally geodesic immersio n of the hyperbolic plane into M. In this talk\nwe will give an overview o f some results which highlight how geometric\,\ntopological\, and arithmet ic properties of M affect the behavior of\ngeodesic planes in M. This talk is based on joint works with McMullen\,\nOh and Margulis.\n LOCATION:https://researchseminars.org/talk/BODS/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Boris Springborn (TU Berlin) DTSTART:20201126T153000Z DTEND:20201126T164500Z DTSTAMP:20260422T225717Z UID:BODS/3 DESCRIPTION:Title: The hyperbolic geometry of Markov's theorem on Diophantine approximation and quadratic forms\nby Boris Springborn (TU Berlin) as part of Bremen Onl ine Dynamics Seminar\n\n\nAbstract\nMarkov's theorem classifies the worst irrational numbers and the most non-zero quadratic forms. This talk is abo ut a new proof using hyperbolic geometry. The main ingredients are a dicti onary to translate between hyperbolic geometry and algebra/number theory\, and some very\nbasic tools borrowed from modern geometric Teichmüller th eory. Simple closed geodesics and ideal triangulations of the modular toru s play an important role\, and so does the problem: How far can a straight line crossing a triangle stay away from the vertices?\n LOCATION:https://researchseminars.org/talk/BODS/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Laura Monk (IRMA\, Strasbourg) DTSTART:20201112T153000Z DTEND:20201112T164500Z DTSTAMP:20260422T225717Z UID:BODS/4 DESCRIPTION:Title: The geometry and spectrum of random hyperbolic surfaces\nby Laura Monk (I RMA\, Strasbourg) as part of Bremen Online Dynamics Seminar\n\n\nAbstract\ nThe main aim of this talk is to present geometric and spectral\npropertie s of typical hyperbolic surfaces. More precisely\, I will:\n\n- introduce a probabilistic model\, first studied by Mirzakhani\, which is\na natural and convenient way to sample random hyperbolic surfaces\n\n- describe the geometric properties of these random surfaces: diameter\,\ninjectivity rad ius\, Cheeger constant\, Benjamini-Schramm convergence...\n\n- explain how one can deduce from this geometric information estimates\non the number o f eigenvalues of the Laplacian in an interval $[a\,b]$\,\nusing the Selber g trace formula.\n LOCATION:https://researchseminars.org/talk/BODS/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Sören Petrat (Jacobs University) DTSTART:20200604T143000Z DTEND:20200604T154500Z DTSTAMP:20260422T225717Z UID:BODS/5 DESCRIPTION:Title: Eff ective Dynamics of the Mean-field Bose Gas\nby Sören Petrat (Jacobs U niversity) as part of Bremen Online Dynamics Seminar\n\n\nAbstract\nThe qu antum dynamics of N non-relativistic bosons is described\nby the Schroedin ger equation with pair interaction. The complexity of\nsolutions generally grow exponentially in the particle number\, so for\nlarge N coarse-graine d or effective descriptions are desirable. From a\nmathematical physics po int of view\, one aims at deriving effective\nequations in a rigorous way\ , i.e.\, proving that their solutions converge\nto the solutions of the Sc hroedinger equation in a suitable topology. In\nthis talk\, we will consid er the dynamics in the mean-field limit\, which\nhas been studied extensiv ely in the last two decades. I will present an\noverview about the researc h goals and results\, and then specifically\ndiscuss recent results of my collaborators and myself on a perturbative\nexpansion of solutions to the Schroedinger equation.\n LOCATION:https://researchseminars.org/talk/BODS/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Keivan Mallahi-Karai (Jacobs University) DTSTART:20200702T143000Z DTEND:20200702T154500Z DTSTAMP:20260422T225717Z UID:BODS/6 DESCRIPTION:Title: Loc ally random groups\nby Keivan Mallahi-Karai (Jacobs University) as par t of Bremen Online Dynamics Seminar\n\n\nAbstract\nGroups without non-triv ial low dimensional representations\,\nnamed quasi-random by Gowers\, have recently found many applications in\nstudying group theoretical problems of combinatorial nature. Loosely\nspeaking\, non-existence of such repres entations forces the product map\non the group mapping $(a\, b)$ to their product $ab$ to have a certain mixing\nbehavior.\n\nIn this talk\, after b riefly recalling the notion of quasi randomness\, I\nwill discuss a gener alisation of this concept to the class of compact\ngroups. This property\, called local randomness\, is formulated in terms\nof unitary representati ons of the compact group $G$ and captures a similar\nmixing behavior at al l scales. I will discuss a number of related\nresults including a classif ication of locally random groups\, a mixing\ninequality\, and\, if time al lows\, connection to spectral gap.\n\nThe talk is based on a joint work wi th Amir Mohammadi and Alireza Salehi\nGolsefidy.\n LOCATION:https://researchseminars.org/talk/BODS/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrew Mitchell (University of Birmingham) DTSTART:20210218T153000Z DTEND:20210218T164500Z DTSTAMP:20260422T225717Z UID:BODS/7 DESCRIPTION:Title: Mea sure theoretic entropy of random substitutions\nby Andrew Mitchell (Un iversity of Birmingham) as part of Bremen Online Dynamics Seminar\n\n\nAbs tract\nRandom substitutions and their associated subshifts provide\na mode l for structures that exhibit both long range order and positive\nentropy. In this talk we discuss the entropy of a large class of ergodic\nmeasures \, known as frequency measures\, that arise naturally from random\nsubstit utions. We introduce a new measure of complexity\, namely measure\ntheore tic inflation word entropy\, and discuss its relationship to\nmeasure theo retic entropy. We also show how this new measure of\ncomplexity can be us ed to provide a framework for the systematic study\nof the measure theoret ic entropy of random substitution subshifts.\n\nAs an application of our r esults\, we obtain closed form formulas for the\nentropy of a wide range o f random substitution subshifts and show that\nin many cases there exists a frequency measure of maximal entropy.\nFurther\, for a class of random s ubstitution subshifts\, we show that this\nmeasure is the unique measure o f maximal entropy.\n\nThis is joint work with P. Gohlke\, R. Leek\, D. Rus t\, and T. Samuel.\n LOCATION:https://researchseminars.org/talk/BODS/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Carlangelo Liverani (U Roma „Tor Vergata“) DTSTART:20210209T130000Z DTEND:20210209T143000Z DTSTAMP:20260422T225717Z UID:BODS/9 DESCRIPTION:Title: Mea surements in Dynamical Systems\nby Carlangelo Liverani (U Roma „Tor Vergata“) as part of Bremen Online Dynamics Seminar\n\n\nAbstract\nVery often a measurement of a physical system takes the form of a finite\ntime average for some observable. For infinite time averages Birkhoff's\ntheore m classifies all the possible outcomes in terms of the invariant\nmeasures of the system. The study of the\, much more realistic\, finite\ntime aver ages is equivalent to investigating at which speed the limit is\nattained. This problem is only partially understood\, essentially we\nunderstand fe w special cases. Yet\, our current knowledge shows that the\nbehaviour dep ends drastically from the properties of the system. In the\nstudy of such a problem functional analysis\, probability theory\, and\ngeometry play ma jor roles. I will attempt to give an overview of the\nsubject.\n\nThis is a joint event with the mathematical colloquium at the\nUniversity of Breme n\n LOCATION:https://researchseminars.org/talk/BODS/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Barbara Schapira (Université Rennes 1) DTSTART:20210315T143000Z DTEND:20210315T154500Z DTSTAMP:20260422T225717Z UID:BODS/10 DESCRIPTION:Title: St rong positive recurrence for geodesic flows\nby Barbara Schapira (Univ ersité Rennes 1) as part of Bremen Online Dynamics Seminar\n\n\nAbstract\ nIn a recent paper with S Gouezel and S Tapie\, in the context of geodesic \nflows of noncompact negatively curved manifolds\, we propose three\ndiff erent definitions of entropy and pressure at infinity\, through\ngrowth of periodic orbits\, critical exponents of Poincaré series\, and\nentropy ( pressure) of invariant measures. We show that these notions\ncoincide. Tha nks to these entropy and pressure at infinity\, we\ninvestigate thoroughly the notion of strong positive recurrence in this\ngeometric context. A po tential is said strongly positively recurrent\nwhen its pressure at infini ty is strictly smaller than the full\ntopological pressure. We show in par ticular that if a potential is\nstrongly positively recurrent\, then it ad mits a finite Gibbs measure. We\nalso provide easy criteria allowing to bu ild such strong positively\nrecurrent potentials and many examples.\n\nDur ing the talk\, I will present some of these points\, to give to the\naudie nce the flavour of this work.\n LOCATION:https://researchseminars.org/talk/BODS/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Péter Koltai (FU Berlin) DTSTART:20210419T133000Z DTEND:20210419T144500Z DTSTAMP:20260422T225717Z UID:BODS/11 DESCRIPTION:Title: Co arse-graining of transport in non-autonomous systems\nby Péter Koltai (FU Berlin) as part of Bremen Online Dynamics Seminar\n\n\nAbstract\nThe decomposition of the state space of a dynamical system into almost\ninvari ant sets is important for understanding its essential macroscopic\nbehavio r. The concept is reasonably well understood for autonomous\ndynamical sys tems\, and recently a generalization appeared for\nnon-autonomous systems: coherent sets. Aiming at a unified theory\, in\nthis talk we will first p resent connections between the\nmeasure-theoretic autonomous and non-auton omous concepts. We shall do\nthis by considering the augmented state space . Second\, we will extend\nthe framework to finite-time systems\, and show that it is especially\nwell-suited for manipulating the mixing properties of the dynamics.\nThird\, we will show how this framework can be used to identify the birth\nand death of coherent sets.\n LOCATION:https://researchseminars.org/talk/BODS/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Valérie Berthé (CNRS\, IRIF\, Université de Paris) DTSTART:20210531T133000Z DTEND:20210531T144500Z DTSTAMP:20260422T225717Z UID:BODS/12 DESCRIPTION:Title: Mu ltidimensional continued fractions and symbolic codings of toral translati ons\nby Valérie Berthé (CNRS\, IRIF\, Université de Paris) as part of Bremen Online Dynamics Seminar\n\n\nAbstract\nIt has been a long standi ng problem to find good symbolic codings for\nKronecker toral translatio ns that enjoy the beautiful properties\nof Sturmian sequences like low fa ctor complexity and good local\ndiscrepancy properties. \nWe construct suc h codings in terms of multidimensional continued fraction\nalgorithms that are realized by sequences of substitutions. In particular\,\ngiven any st rongly convergent continued fraction algorithm\, these sequences\nlead to renormalization schemes which produce symbolic codings and bounded\nremain der sets at all scales in a natural way. Such sets \nprovide particular ly strong convergence properties of ergodic sums\, \nand are also closel y related to the notion of balance in word\ncombinatorics. \n As strong c onvergence of a continued fraction algorithm results in a Pisot\ntype prop erty\, our approach provides a systematic way to confirm purely\ndiscrete \nspectrum results for wide classes of substitutions.\nThis is joint wor k with W. Steiner and J. Thuswaldner.\n LOCATION:https://researchseminars.org/talk/BODS/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Ilya Gekhtman (Technion) DTSTART:20210308T143000Z DTEND:20210308T154500Z DTSTAMP:20260422T225717Z UID:BODS/13 DESCRIPTION:Title: Gi bbs measures vs. random walks in negative curvature\nby Ilya Gekhtman (Technion) as part of Bremen Online Dynamics Seminar\n\n\nAbstract\nThe id eal boundary of a negatively curved manifold naturally\ncarries two types of measures.\nOn the one hand\, we have conditionals for equilibrium (Gibb s) states\nassociated to Hoelder potentials\; these include the Patterson- Sullivan\nmeasure and the Liouville measure. On the other hand\, we have s tationary\nmeasures coming from random walks on the fundamental group.\n We compare and contrast these two classes.First\, we show that both\nof t hese of these measures can be associated to geodesic flow invariant\nmeasu res on the unit tangent bundle\, with respect to which closed\ngeodesics s atisfy different equidistribution properties. Second\, we show\nthat the a bsolute continuity between a harmonic measure and a Gibbs\nmeasure is equi valent to a relation between entropy\, (generalized)\ndrift and critical exponent\, generalizing previous formulas of\nGuivarc’h\, Ledrappier\, a nd Blachere-Haissinsky-Mathieu. This shows that\nif the manifold (or more generally\, a CAT(-1) quotient) is geometrically\nfinite but not convex co compact\, stationary measures are always singular\nwith respect to Gibbs m easures.\nA major technical tool is a generalization of a deviation inequa lity due\nto Ancona saying the so called Green distance associated to the random\nwalk is nearly additive along geodesics in the universal cover.\nP art of this is based on joint work with Gerasimov-Potyagailo-Yang and\npar t on joint work with Tiozzo.\n LOCATION:https://researchseminars.org/talk/BODS/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Giulio Tiozzo (University of Toronto) DTSTART:20210322T143000Z DTEND:20210322T154500Z DTSTAMP:20260422T225717Z UID:BODS/14 DESCRIPTION:Title: Th e fundamental inequality for random walks on cocompact Fuchsian groups \nby Giulio Tiozzo (University of Toronto) as part of Bremen Online Dynami cs Seminar\n\n\nAbstract\nSeveral stochastic processes are defined on the hyperbolic plane H^2. For instance\, one can consider a Brownian motion\, or a discretized version thereof\, when one performs a random walk on the group of isometries of H^2. \n\nIt is a recurring question\, going back to Furstenberg\, Guivarc’h\, Ledrappier\, Kaimanovich\, and others\, \nwhe ther the measures obtained from the random walks coincide with measures of geometric origin\, such as the Lebesgue measure. \n\nWe prove that the hi tting measure is singular with respect to Lebesgue measure for any random walk on a cocompact Fuchsian group generated by translations on opposite s ides of a symmetric hyperbolic polygon. This addresses a question of Kaima novich-Le Prince. \n\nJoint with P. Kosenko.\n LOCATION:https://researchseminars.org/talk/BODS/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Rhiannon Dougall DTSTART:20210517T133000Z DTEND:20210517T144500Z DTSTAMP:20260422T225717Z UID:BODS/15 DESCRIPTION:Title: Co mparison of entropy for infinite covering manifolds\, and group extensions of subshifts of finite type\nby Rhiannon Dougall as part of Bremen On line Dynamics Seminar\n\n\nAbstract\nA classical example of an Anosov flow is the geodesic flow associated to\na compact hyperbolic manifold M\, for which the periodic orbits of the\nflow correspond to closed geodesics in M. In general\, Anosov flows are\nnot so well behaved: there may be infini tely many periodic orbits in a\nfree homotopy class\, in contract to geode sic flows. In this talk we\ndiscuss the problem of counting periodic orbit s in infinite covering\nmanifolds\, where we relate the exponential growth rate of periodic\norbits in the cover to properties of the covering group . One of the\ntools is a new result for non-symmetric group extensions of subshifts of\nfinite type which includes a result on non-symmetric random walks. I\nwill spend some time motivating the problems and give the perspe ctive of\nthe thermodynamical formalism.\n(Featuring joint work with Richa rd Sharp.)\n LOCATION:https://researchseminars.org/talk/BODS/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Ilka Agricola (Uni Marburg) DTSTART:20210608T140000Z DTEND:20210608T151500Z DTSTAMP:20260422T225717Z UID:BODS/16 DESCRIPTION:Title: Wh at are spinors and what should they be?\nby Ilka Agricola (Uni Marburg ) as part of Bremen Online Dynamics Seminar\n\n\nAbstract\nRichard Dedekin d published in 1888 a paper entitled "Was sind und was sollen\ndie Zahlen? "\, variously translated as "What are numbers and what should\nthey be?". In analogy to this classic\, I shall investigate in this talk\nwhat spinor s (or\, in full term\, spinor fields) are\, what distinguishes\nthem from functions\, how they appear naturally in complex analysis and\ntheoretical physics\, and\, finally\, why they are an object of intrinsic\nmathematic al\ninterest. Doing so\, I will give a gentle introduction to spin geometr y\nand Dirac operators for the non-experts\, and I will provide an overvie w of\ntypical problems and interesting links to other areas.\n\nThis is a joint seminar with the University of Bremen Mathematics Colloquium.\n LOCATION:https://researchseminars.org/talk/BODS/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Vlad Vicol (NYU) DTSTART:20210506T140000Z DTEND:20210506T151500Z DTSTAMP:20260422T225717Z UID:BODS/17 DESCRIPTION:Title: Sh ock formation for the 3d Euler equations\nby Vlad Vicol (NYU) as part of Bremen Online Dynamics Seminar\n\n\nAbstract\nIn this talk\, I will dis cuss the shock formation process for the 3d\ncompressible Euler equations\ , in which sounds waves interact with\nentropy waves to produce vorticity. Smooth solutions form a generic\nstable shock with explicitly computable blowup time\, location\, and\ndirection. Our method establishes the asympt otic stability of a generic\nshock profile in modulated self-similar varia bles\, controlling the\ninteraction of three distinct wave families.\n\nTh is is based on joint work with T. Buckmaster and S. Shkoller.\n LOCATION:https://researchseminars.org/talk/BODS/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Seonhee Lim (Seoul National University) DTSTART:20210614T080000Z DTEND:20210614T091500Z DTSTAMP:20260422T225717Z UID:BODS/18 DESCRIPTION:Title: Br ownian motion in negative curvature\nby Seonhee Lim (Seoul National Un iversity) as part of Bremen Online Dynamics Seminar\n\n\nAbstract\nBrownia n motion in the hyperbolic space $H^n$ is rather\nwell-known with a precis e formula for the heat kernel\, which is the\nprobability density function of the Brownian motion. In this talk\, we\nwill talk about the asymptotic formula for the heat kernel in a\nconnected simply connected negatively c urved Riemannian manifold X whose\nmetric is lifted from a compact manifol d M.\n As time goes to infinity\, we show that the heat kernel $p(t\,x\,y) $ is\nasymptotically $e^{-\\lambda_0} t^{-3/2} C(x\,y)$ where $\\lambda_0$ is the\nbottom of the spectrum of the geometric Laplacian. The proof uses the\nuniform Harnack inequality on the boundary $\\partial X$ as well as the\nuniform mixing of the geodesic flow on the quotient manifold M. (This is\na joint work with François Ledrappier.)\n LOCATION:https://researchseminars.org/talk/BODS/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Wael Bahsoun (Loughborough) DTSTART:20210712T133000Z DTEND:20210712T144500Z DTSTAMP:20260422T225717Z UID:BODS/19 DESCRIPTION:Title: Tr ansfer operators and BV spaces: from classic to anisotropic\nby Wael B ahsoun (Loughborough) as part of Bremen Online Dynamics Seminar\n\n\nAbstr act\nSmooth ergodic theory aims to analyse the long-term statistics\nof ch aotic dynamical systems. There are several analytic and\nprobabilistic too ls that are used to answer such questions. Each of\nthese approaches has i ts advantages and its shortcomings\, depending on\nthe system under consid eration. In this presentation\, I will focus on\ntransfer operator techniq ues and spectral methods\, which are known to be\nvery powerful when deali ng with uniformly expanding\, or uniformly\nhyperbolic systems. The first half of this talk will be rather\nintroductory\, aimed at non-experts\, fo cusing on ideas behind this\napproach through simple\, yet important examp les. In the second half of\nthe talk\, I will discuss a recent joint work with C. Liverani\, whose\nlong-term goal is to provide a good spectral pic ture for piecewise\nhyperbolic systems with singularities (e.g. billiard m aps) in any\ndimension. In connection with this goal\, I will also discuss a recent\njoint work with F. Sélley on coupled map lattices.\n LOCATION:https://researchseminars.org/talk/BODS/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Folkmar Bornemann (TU München) DTSTART:20210726T133000Z DTEND:20210726T144500Z DTSTAMP:20260422T225717Z UID:BODS/20 DESCRIPTION:Title: Fi nite size effects: random matrices\, quantum chaos\, and Riemann zeros \nby Folkmar Bornemann (TU München) as part of Bremen Online Dynamics Sem inar\n\n\nAbstract\nSince the legendary 1972 encounter of H. Montgomery an d F.\nDyson at tea time in Princeton\, a statistical correspondence of the \nnon-trivial zeros of the Riemann Zeta function with eigenvalues of\nhigh -dimensional random matrices has emerged. Surrounded by many deep\nbut not oriously intractable conjectures\, there is a striking analogy to\nthe ene rgy levels of a quantum billiard system with chaotic dynamics.\nThe statis tical accuracy provided by an enormous dataset of more than\none billion z eros reveals distinctive finite size effects. Using the\nphysical analogy\ , we discuss a precise prediction of these effects that\nhas been obtained in terms of operator determinants and their\nperturbation series (joint w ork with P. Forrester and A. Mays\, Melbourne).\n LOCATION:https://researchseminars.org/talk/BODS/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Sergey Zelik (University of Surrey) DTSTART:20210913T133000Z DTEND:20210913T144500Z DTSTAMP:20260422T225717Z UID:BODS/21 DESCRIPTION:Title: De terministic and random attractors for a wave equation with sign changing d amping\nby Sergey Zelik (University of Surrey) as part of Bremen Onlin e Dynamics Seminar\n\n\nAbstract\nWe discuss the long-time dynamics gener ated\nby weakly damped wave equations in bounded 3D domains where\nthe dam ping coefficient depends explicitly on time and may change sign.\nWe show that in the case when the non-linearity is super-linear\, the\nconsidered equation remains dissipative if the weighted mean value of\nthe dissipatio n rate remains positive and that the conditions of this type\nare not suff icient in the linear case. Two principally different cases will be\nconsi dered. In the case when this mean is uniform (which corresponds\nto determ inistic dissipation rate)\, it will be shown that the considered system\np ossesses smooth uniform attractors as well as non-autonomous exponential\n attractors. In the case where the mean is not uniform (which\ncorresponds to the random dissipation rate\, for instance\, when this dissipation\nrat e is generated by the Bernoulli process)\, the tempered random\nattractor will be constructed. In contrast to the usual situation\, this\nrandom att ractor is expected to have infinite Hausdorff \nand fractal dimensions. T he simplified model example which demonstrates in\nfinite-dimensionality of the random attractor will also be presented.\n LOCATION:https://researchseminars.org/talk/BODS/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Jon Aaronson (Tel Aviv University) DTSTART:20211129T143000Z DTEND:20211129T154500Z DTSTAMP:20260422T225717Z UID:BODS/22 DESCRIPTION:Title: Re newal and ratio mixing properties of "nice" infinite ergodic transformatio ns\nby Jon Aaronson (Tel Aviv University) as part of Bremen Online Dyn amics Seminar\n\n\nAbstract\nI'll discuss "ratio mixing" properties\nof transformations preserving infinite measures ( e.g. as in Hopf's\n1936 bo ok) and also their "renewal properties"\n(occupation processes to sets of finite measure). Examples of "nice"\ntransformations considered include ce rtain null-recurrent Markov\nchains\, - "intermittent" interval maps\, - i nner functions\, hyperbolic\ngeodesic flows on cyclic covers.\n\nIncludes joint work with Hitoshi Nakada\, Dalia Terhesiu & Toru Sera.\n LOCATION:https://researchseminars.org/talk/BODS/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Mikhail Hlushchanka (Utrecht University) DTSTART:20220110T143000Z DTEND:20220110T154500Z DTSTAMP:20260422T225717Z UID:BODS/23 DESCRIPTION:Title: Ca nonical decomposition of rational maps\nby Mikhail Hlushchanka (Utrech t University) as part of Bremen Online Dynamics Seminar\n\n\nAbstract\nThe re are various classical and more recent decomposition results in mapping class group theory\, geometric group theory\, and complex dynamics (which include celebrated results by Bill Thurston). The goal of this talk is to introduce a novel powerful decomposition of rational maps based on the top ological structure of their Julia sets. Namely\, we will discuss the follo wing result: every postcritically-finite rational map with non-empty Fatou set can be canonically decomposed into crochet maps (these have very "thi nly connected" Julia sets) and Sierpinski carpet maps (these have very "he avily connected" Julia sets). If time permits\, I will discuss application s of this result in various aspects of geometric group theory. Based on a joint work with Dima Dudko and Dierk Schleicher.\n LOCATION:https://researchseminars.org/talk/BODS/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Tushar Das (University of Wisconsin-La Crosse) DTSTART:20220131T143000Z DTEND:20220131T154500Z DTSTAMP:20260422T225717Z UID:BODS/24 DESCRIPTION:Title: Di mension theory for infinite-alphabet conformal iterated function system li mit sets\nby Tushar Das (University of Wisconsin-La Crosse) as part of Bremen Online Dynamics Seminar\n\n\nAbstract\nStudying the extremely deli cate geometric-measure-theoretic properties of dynamical limit sets is oft en an endeavor beset with myriad challenges. In this vein\, we focus on th e dimension-theoretic study of continued fraction Cantor sets -- a rich se am inaugurated by the work of Jarník and Besicovitch in the 1920s. I will report on two projects about such fascinating fractals. The first conside rs small perturbations of a conformal iterated function system (CIFS)\; wh ile the second resolves two recent questions posed by Chousionis\, Leykekh man\, and Urbański regarding the dimension spectrum of a CIFS (i.e. the s et of all Hausdorff dimensions of its various subsystem limit sets). We ho pe to present several interesting problems and directions that await resol ution and explorations by the brilliant Bremen dynamics group 🙂\n LOCATION:https://researchseminars.org/talk/BODS/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Anja Randecker (University of Heidelberg) DTSTART:20220117T143000Z DTEND:20220117T154500Z DTSTAMP:20260422T225717Z UID:BODS/26 DESCRIPTION:Title: In terval exchange transformations and translation surfaces in genus 2\nb y Anja Randecker (University of Heidelberg) as part of Bremen Online Dynam ics Seminar\n\n\nAbstract\nTranslation surfaces arise naturally in many di fferent contexts such as the theory of mathematical billiards\, of Teichm üller spaces\, or of stability conditions of categories.\nA translation s urface can be described by finitely many polygons that are glued along edg es which are parallel and have the same length.\n\nFrom a dynamical system point of view\, it is interesting to study the geodesic flow on translati on surfaces. These flows are strongly related to interval exchange transfo rmations.\n\nIn my talk\, I will explain this relation and give an explici t description of translation surfaces of genus 2 where the horizontal geod esic flow is completely periodic. The talk is based on joint work in progr ess with Binbin Xu.\n LOCATION:https://researchseminars.org/talk/BODS/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Claire Burrin (ETH Zurich) DTSTART:20220214T143000Z DTEND:20220214T154500Z DTSTAMP:20260422T225717Z UID:BODS/27 DESCRIPTION:Title: Wi ndings of closed geodesics and number theory\nby Claire Burrin (ETH Zu rich) as part of Bremen Online Dynamics Seminar\n\n\nAbstract\nIn his 2006 ICM lecture\, Ghys made the following observation: the winding of a close d geodesic around the cusp of the modular surface can be computed using a function from the theory of modular forms\; the Rademacher function. In jo int work with Flemming von Essen\, we studied how and when generalizations of the Rademacher function also encode the winding for closed geodesics a round the cusps of hyperbolic surfaces. For certain families of surfaces\, we use a Selberg trace formula argument to obtain precise statistical res ults on these winding numbers.\n LOCATION:https://researchseminars.org/talk/BODS/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Jonathan Ben-Artzi (Cardiff University) DTSTART:20220523T133000Z DTEND:20220523T144500Z DTSTAMP:20260422T225717Z UID:BODS/28 DESCRIPTION:Title: Dy namical systems lacking spectral gaps: functional inequalities and converg ence rates\nby Jonathan Ben-Artzi (Cardiff University) as part of Brem en Online Dynamics Seminar\n\n\nAbstract\nOur world is neither compact nor periodic. It is therefore natural to consider dynamical systems on unboun ded domains\, where typically there is no spectral gap. I will present a ( simple) method for studying the generators of such systems where a spectra l gap assumption is replaced with an estimate of the Density of States (Do S) near zero. There are two main applications:\n\n1) Dissipative systems: when the generator is non-negative\, an estimate of the DoS leads to a so- called "weak Poincaré inequality" (WPI). This in turn leads (in some case s) to an algebraic decay rate for the $L^2$ norm of the solution. For inst ance\, in the case of the Laplacian (generator of the heat equation) the W PI is simply the Nash inequality which leads to the optimal decay rate of $t^{-d/4}$.\n\n2) Conservative systems: when the generator is skew-adjoint \, an estimate of the DoS leads to a uniform ergodic theorem on an appropr iate subspace. Examples include the linear Schrödinger equation and incom pressible flows in Euclidean space.\n\nBased on joint works with Amit Eina v (Durham) and Baptiste Morisse (formerly a postdoc at Cardiff).\n LOCATION:https://researchseminars.org/talk/BODS/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Shayan Alikhanloo (Uni Bielefeld) DTSTART:20220321T143000Z DTEND:20220321T154500Z DTSTAMP:20260422T225717Z UID:BODS/29 DESCRIPTION:Title: Se lf-adjoint Laplacians\, symmetric semigroups and diffusions on hyperbolic attractors\nby Shayan Alikhanloo (Uni Bielefeld) as part of Bremen Onl ine Dynamics Seminar\n\n\nAbstract\nAnalysis on smooth manifolds\, foliate d spaces and fractals in terms of Dirichlet forms is well established. But such an analysis on hyperbolic attractors is yet to be explored. We use t he core material and central results from the theory of hyperbolic dynamic al systems such as the stable manifold theorem and physical measures to in troduce self-adjoint Laplacians\, symmetric Markov semigroups and symmetri c diffusions via Dirichlet forms. In particular\, this may be seen as far- reaching extension of well-known classical analysis on geodesic flows on m anifolds of negative sectional curvature. This talk is based on a joint wo rk with Michael Hinz.\n LOCATION:https://researchseminars.org/talk/BODS/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Luca Marchese ((University of Bologna)) DTSTART:20220718T133000Z DTEND:20220718T144500Z DTSTAMP:20260422T225717Z UID:BODS/30 DESCRIPTION:Title: Tr ansfer operators and dimension of bad sets for non-uniform fuchsian lattic es\nby Luca Marchese ((University of Bologna)) as part of Bremen Onlin e Dynamics Seminar\n\n\nAbstract\nThe set of badly approximable real numbe rs admits an exhaustion in sets Bad(c) with c>0\, whose dimension goes to zero as c goes to zero. D. Hensley computed the asymptotic for the dimensi on up to the first order in c\, via an estimate for the dimension of the s et of real numbers whose continued fraction has partial quotiens bounded b y a fixed parameter. We consider diophantine approximations by parabolic f iwed points of any non-uniform lattice in PSL(2\,R) and the corresponding notion of badly approximable real numbers. We compute the dimension of the set of such points up to the first order in c>0\, via the thermodynamic m ethod of Ruelle and Bowen. Geometric good approximations are related to a notion of bounded partial quotients for the Bowen-Series expansion. This g ives a family of Cantor sets and associated quasi-compact transfer operato rs\, with simple and positive maximal eigenvalue. Then perturbative analys is of spectra applies.\n LOCATION:https://researchseminars.org/talk/BODS/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Pouya Mehdipour (Universidade Federal de Viçosa) DTSTART:20260417T150000Z DTEND:20260417T160000Z DTSTAMP:20260422T225717Z UID:BODS/31 DESCRIPTION:Title: Ex tended Symbolic Dynamics: Some Applications and Future Perspectives\nb y Pouya Mehdipour (Universidade Federal de Viçosa) as part of Bremen Onli ne Dynamics Seminar\n\n\nAbstract\nWe introduce zip shift maps as local ho meomorphisms that extend symbolic dynamics of the two-sided shift type. Us ing examples of finite-to-one horseshoe maps\, we show how these systems c an be fully coded\, up to topological conjugacy\, by such symbolic structu res. We also explore applications in ergodic theory\, topological dynamics \, and cellular automata\, and discuss potential future directions for the ir development and use in related fields.\n LOCATION:https://researchseminars.org/talk/BODS/31/ END:VEVENT END:VCALENDAR